# Quantum scattering - 1/r^2

1. Dec 7, 2008

### neworder1

1. The problem statement, all variables and given/known data

Use partial waves method to calculate scattering amplitude for a quantum particle scattering off the potential V(r) = a/r^2.

2. Relevant equations

3. The attempt at a solution

To calculate phase shifts $$\delta_{l}$$ for each angular momentum's value l, it's necessary to solve Schrodnger's equation for the specified potential - but I'm unable to do it. I know that solution for a free particle can be expressed in terms of Bessel spherical functions, but in radial Schrodinger's equation we have the centrifugal term of the form l(l+1)/r^2, where l is an integer, not for arbitary potential a/r^2. Any hints?

2. Dec 7, 2008

### Avodyne

The radial equation doesn't care whether or not l is an integer ...

3. Dec 7, 2008

### neworder1

Ok, but in the noninteger case the solutions are special functions, from which I don\t know how to calculate the phase factors in question.

4. Dec 7, 2008

### Avodyne

The asymptotic properties of Bessel functions hold whether or not the index is an integer.